Rewrite as a simplified fraction. ${0.\overline{91} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 91.9191...\\ 1x &= 0.9191...\end{align*}}$ Subtracting the two equations, we have: ${99x = 91}$ ${x = \dfrac{91}{99}} $